Please use this identifier to cite or link to this item: http://hdl.handle.net/10553/47213
Title: A direct solver for the least‐squares problem arising from GMRES(k)
Authors: Galán, Manuel J.
Montero, Gustavo 
Winter, Gabriel 
UNESCO Clasification: 1206 Análisis numérico
Issue Date: 1994
Journal: Communications in Numerical Methods in Engineering 
Abstract: This is a study about one of the core questions in the GMRES(k) method regarding the obtaining of vector yk for the least‐squares problem, argminy |Hky ‐ β(n)e1|2 (see Saad and Schultz1). We propose a simple but efficient approach to the resolution of this problem and a low cost computation of the residual and the residual norm, including both in a complete and detailed FGMRES(k) algorithm. The whole algorithm of minimization only involves two backward substitutions with triangular matrices and a dot product. The residual and the residual norm are computed, making use of results in the least‐squares problem.
URI: http://hdl.handle.net/10553/47213
ISSN: 1069-8299
DOI: 10.1002/cnm.1640100909
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